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linear algebra operations on symbolic vectors and matrices

linear algebra is the study of linear equations and their properties. symbolic math toolbox™ provides functions to solve systems of linear equations. you can also analyze, transform, and decompose matrices using symbolic math toolbox functions.

functions

matrix operations

concatenate symbolic arrays along specified dimension
create symbolic vectors, array subscripting, and for-loop iterators
concatenate symbolic arrays horizontally
sort elements of symbolic arrays
concatenate symbolic arrays vertically

matrix transformations

create diagonal matrix or get diagonals from symbolic matrices
reshape symbolic array
return lower triangular part of symbolic matrix
return upper triangular part of symbolic matrix

solving linear equations

classical adjoint (adjugate) of square matrix
condition number of matrix
determinant of symbolic matrix
convert linear equations to matrix form
inverse of symbolic matrix
solve linear equations in matrix form
norm of symbolic vector or matrix
moore-penrose inverse (pseudoinverse) of symbolic matrix
find rank of symbolic matrix
reduced row echelon form of matrix (gauss-jordan elimination)

matrix basis

basis for column space of matrix
form basis for null space of matrix
orthonormal basis for range of symbolic matrix

matrix factorizations

cholesky factorization
lu factorization
qr decomposition of symbolic matrix
singular value decomposition of symbolic matrix
characteristic polynomial of matrix
eigenvalues and eigenvectors of symbolic matrix
jordan normal form (jordan canonical form)
curl of symbolic vector field
divergence of symbolic vector field
gradient vector of symbolic scalar field
hessian matrix of symbolic scalar function
jacobian matrix of symbolic function
laplacian of symbolic field
potential of vector field
vector potential of vector field

normal forms

hermite form of matrix
jordan normal form (jordan canonical form)
smith form of matrix

special matrices

bernstein matrix
symbolic toeplitz matrix
matrix exponential of symbolic matrices
general matrix function
matrix logarithm
matrix square root

topics


  • this example shows how to perform simple matrix computations using symbolic math toolbox™.


  • perform linear algebra with symbolic expressions and functions.


  • solve systems of linear equations in matrix or equation form.


  • perform algebraic operations on symbolic expressions and function.


  • singular value decomposition (svd) of a matrix.


  • find eigenvalues, characteristic polynomials, and determinants of matrices.


  • convert matrix to jordan normal form (jordan canonical form).


  • this example shows how to solve the eigenvalue problem of the laplace operator on an l-shaped region.


  • this example shows how to compute the inverse of a hilbert matrix using symbolic math toolbox™.

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